Global attractivity of the equilibrium of a nonlinear difference equation

Title:

Global attractivity of the equilibrium of a nonlinear difference equation

Creator:

Graef, John R. and Qian, C.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:cd834820-29ca-49d7-8213-8da1a308a0ac
uuid:cd834820-29ca-49d7-8213-8da1a308a0ac

Subject:

nonlinear difference equation, global attractivity, and oscillation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The authors consider the nonlinear difference equation \[ x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots .1 \text{where} \alpha \in (0, 1),\hspace{5.0pt}k \in \lbrace 0, 1, \dots \rbrace \hspace{5.0pt}\text{and}\hspace{5.0pt}f\in C^1[[0, \infty),[0, \infty )] \qquad \mathrm{(0)}\] with $f^{\prime }(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

757-769

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:4

Harvested from:

CDK

Metadata only:

false